You must first install the Java Runtime Environment (JRE) to run Java applets in K-Meleon. You can download the latest version from http://www.java.com/en/index.jsp. After you install JRE, K-Meleon automatically detects your JRE installation and no other configuration is necessary. To see if JRE is properly installed, type about:plugins in the URL bar. If you see Java Plug-in listed, K-Meleon has properly recognized the JRE.

Note: If you change the User Agent/Browser Identification, Java may not work.

(The above text can be found in the FAQ, too.)

Notes:

by Marc: If java is installed and is working in IE (you should be sure that IE is not using windows/MS older library) but not in KM, or other gecko-based browsers, check your registry. The following key should exist. It should have been created when KM was installed.